Question

$△ABC\sim △DEF$. $△ABC$ is such that $AB=5.2cm,BC=4.6cm$, $\angle B={45}^{\circ }$ and $\frac{BC}{EF}=\frac{2}{3}$; Construct $△DEF$.

Answer 1

The sides of $△DEF$ will be $\frac{3}{2}$ times the sides of $△ABC$

$\therefore DE=\frac{3}{2}\times AB=\frac{3}{2}\times 5.2=7.8cm$

$EF=\frac{3}{2}\times BC=\frac{3}{2}\times 4.6=6.9cm$

Also, $\angle E=\angle B={45}^{\circ }$

Construction:

Step $1$: Draw base $DE=7.8cm$ with a ruler.

Step $2$: Draw a line from $E$ at an angle of ${45}^{\circ }$ with the line $DE$ using a protractor.

Step $3$: Place the compass on point $E$ and measure an arc with length of the compass as $EF=6.9cm$.

Step $4$: Mark the intersection point of the arc with the line as $F$ and join $D-F$.

$△DEF$ is the required triangle.